Wallis's Product/Historical Note

Historical Note on Wallis's Product

Wallis's product was published by John Wallis in $1656$, in his Arithmetica Infinitorum.

Wallis, of course, had no recourse to Euler's techniques.

He did this job by comparing $\ds \int_0^\pi \sin^n x \rd x$ for even and odd values of $n$, and noting that for large $n$, increasing $n$ by $1$ makes little change.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.12$: Wallis's Product
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Wallis's product